Lesson Outline:

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Lesson Outline
I. Review of Math Skills
II. Scientific Notation
III. The Metric System
IV. Reading Graphs
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Unit Conversions
An efficient method for converting a measurement
from one unit into another is known as unit
analysis.
The key is to identify an appropriate conversion
ratio, or sequence of ratios, and keeping track
of the units.
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Example 1
The average depth of the worlds oceans is 12,500
feet. Convert this to miles.
Since there are 5,280 feet in one mile
2.37 mi
Note that multiplying the depth by the unit ratio
only changes the units of the depth, not the
depth itself, since we are multiplying by 1.
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Example 2
Some conversions may require multiplying by more
than one ratio.
Convert the depth of 12,500 feet to meters.
The necessary conversion factors are
1 ft 12 in, 1 in 2.54 cm, and 1 m 100 cm.
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Measuring Temperature
Temperature can measured on the Fahrenheit scale
or the Celsius or Centigrade scale.
On the Fahrenheit scale, pure water freezes at
32º F and boils at 212º F.
On the Celsius scale, pure water freezes at 0º C
and boils at 100º C.
Since the zero points on these scales represent
different temperatures, the method of unit
analysis does not work for temperature
conversions.
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Converting Temperatures
For converting temperatures from one system to
the other we use the formulas
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Example 3
(a) Convert 50º F to Celsius
Substitute F 50 into the first equation to get
Thus, 50º F 10º C.
(b) Convert 45º C to Fahrenheit
Substitute C 45 into the second equation to get
Thus, 45º C 113º F.
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Scientific Notation
Because oceanographers study phenomena that occur
over very large and very small scales, scientific
measurements may involve extremely large and
small numbers.
A concise and easy means of representing
measurements of such magnitude is through the use
of scientific notation.
Scientific notation uses powers of 10 in place of
the long sequence of zeros before or after the
decimal point.
A large or small number is expressed as a number
between 1 and 10 multiplied by an appropriate
power of 10.
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Example
(a) Express the number 1,220,000 in scientific
notation.
For numbers greater than 10, the power of ten is
positive.
(b) Express the number .0000122 in scientific
notation.
For numbers less than 1, the power of ten is
negative.
Note that the power of 10 is the number of places
the decimal point is moved when converting to
scientific notation.
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The Metric System
In the metric system, all measures have a basic
unit.
All other units are related to the basic unit by
some power of ten, which is referred to by a
specific prefix.
Each unit and prefix also has a standard
abbreviation.
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Measuring Length in the Metric System
The basic unit of length in the metric system is
the meter (m).
For reference, 1 meter 39.37 inches
Long distances are often measured in kilometers
(km), which are 1000 meters in length.
Smaller lengths may be measured incentimeters
(cm), which are 1/100 of a meter millimeters
(mm), which are 1/1000 of a meter
Microscopic lengths, can be measured in microns
(µm), which are one-millionth of a meter
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Measuring Mass (Weight) in the Metric System
The basic unit of mass (weight) is the gram (g).
For reference, a paper clip weighs about one
gram.
Larger masses may be measured inkilograms (kg),
which are 1000 grams (1 kg 2.2 lb) metric tons
(t), which are 1,000,000 grams (1 t 2200 lb)
Smaller masses are often measured in milligrams
(mg), which are 1/1000 of a gram.
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Measuring Volume in the Metric System
The basic unit of volume is the liter (L).
For reference, a liter as a little more than one
quart (1 L 1.1 qt).
Smaller volumes are measured in milliliters (mL),
which are 1/1000 of a liter.
A milliliter is also equivalent to a cubic
centimeter (cc or cm³).
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Example 4
(a) Convert 950 milliliters to liters.
(b) Convert 2.15 kilometers to centimeters.
Note that only the position of the decimal point
changes in the answer.
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Reading Graphs
Mathematical equations are one way to specify the
relationships among variable quantities in
oceanography, but these can be quite complicated
or difficult to determine.
In many instances, quantitative relationships are
more easily analyzed through the use of graphs.
Line plots are used to illustrate the
relationship between two varying quantities,
known as the independent and dependent variables.

The independent variable is generally represented
on the horizontal axis, while the dependent
variable is measured on the vertical axis.
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Example 4 Reading a Sea Level Plot
(a) Estimate the highest and the lowest observed
sea levels during the five-day period shown.
Highest 1.1 m
Lowest .35 m
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Example 4 Reading a Sea Level Plot
(b) Estimate the times of the predicted low tides
on 12/24.
Low tides 6 am and 6 pm
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Example 4 Reading a Sea Level Plot
(c) On which day(s) is the observed water level
higher than the predicted water level? On which
day(s) is it lower?
The tides were higher than predicted on 12/23 and
12/24.
They were lower than predicted on 12/25 and 12/26.
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Vertical Profiles
In a vertical profile, the independent variable
is the ocean depth, which is plotted on the
vertical axis with the sea surface at the top.
The dependent variable is plotted on the
horizontal axis with increasing values to the
right.
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Example 5 Reading a Salinity Profile
The figure to the right is a typical vertical
profile of the salinity in the South Atlantic
Ocean.
(a) Estimate the salinity at the ocean surface.
35.5
(b) Estimate the salinity at a depth of 3000
meters.
Approximately 34.7
(c) What is the minimum salinity and at what
depth does it occur?
Approximately 34.3 at a depth of 700 m.
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Field Plots
Field plots are used to visually illustrate the
relationships between three variables, two
independent and one dependent.
The values of the independent variables are
represented on the axes, while the values of the
dependent variable are identified from level
curves (or contours) plotted in the plane.
One example is the bathymetry map of the sea
floor in the Gulf of Mexico off the coast of
Florida. (The root bathy refers to depth).
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Example 6 Reading a Bathymetry Plot
Use the bathymetry map to answer the following
questions
(a) Estimate the water depth at latitude N 28º
45, longitude W 85º 00.
Depth is between 50 m and 100 m.
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Example 6 Reading a Bathymetry Plot
Use the bathymetry map to answer the following
questions
(b) Approximate the increase in water depth
between points A and B.
The depth increases by 2000 m.
(c) Approximate the increase in water depth
between points P and Q.
The depth increases by only 450 m.
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Color Scale
Often a color scale is employed to identify the
values of the dependent variable.
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Example 7 Using a Color Scale
The field plot illustrates how the temperate
varies with depth across the equatorial Atlantic
Ocean.
(a) Estimate the temperature at a depth of 300
meters at longitude 345º.
11º C
(b) Estimate the depth of the 25º C isotherm in
the western Atlantic at longitude 320º.
80 m
(c) Estimate the depth of the 25º C isotherm in
the eastern Atlantic at longitude 360º.
40 m